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Balancedness of Integer Domination Games

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Abstract

In this paper, we consider cooperative games arising from integer domination problem on graphs. We introduce two games, $\{k\}$-domination game and its monotonic relaxed game, and focus on their cores. We first give characterizations of the cores and the relationship between them. Furthermore, a common necessary and sufficient condition for the balancedness of both games is obtained by making use of the technique of linear programming and its duality.

참고문헌 (10)

  1. "\it Some applications of the methods of linear programming to the theory of cooperative games}", pp.119~ (1963)
  2. "it Cooperative game theory and applications. Cooperative games arising from combinatorial optimization problems" (1997), Kluwer Academic Publishers
  3. "it Algorithmic aspects ofthe core of combinatorial optimization games", pp.751~ (1999)
  4. "it Partition games and the core of hierarchically convex cost games" (1995), Universiteit Twente
  5. "A guide to the theory of NP-completeness. A Series of Books in the Mathematical Sciences. W. H. Freeman and Co." (1979)
  6. "it Fundamentals of domination in graphs" (1998), Inc.
  7. "it Domination in graphs. Advanced topics" (1998), Inc.
  8. "\it On the core of linear production games}", pp.358~ (1975)
  9. "\it On balanced sets and cores}", pp.453~ (1967)
  10. "it Dominating set game", pp.565~ (2004)

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